I've had similar issues with my Nexus 4 16GB. Using Solovei (T-Mobile MVNO) in the Phoenix area.
Signal is fine and stable when it is sitting on the table, but goes to heck when I pick it up. H->3G->H->grey bars->pings drop->H->3G
I have been using the free app "GSM Signal Monitoring" which show a perfectly smooth line, until I pick the phone up, at which point the signal starts going crazy, cratering out, thrashing between towers, etc.
I've factory reset, held power for 10s to cause the system to "battery pull" reset, nothing seems to help. The 1.1MB system update Google pushed this morning didn't seem to have any positive effect.
Here are a few screenshots where you can see what is happening. Towards the left of the graphs, the device is sitting stable. To the right, I pick it up while still holding it in the same general area.
This isn't specific to the one area I am in now, it can be seen across town.